Digital measuring techniques offer attractive alternatives to traditional analog methods for the measurement of AC signals. This is especially true where the sampling rate obtainable is high with respect to the period of the signal to be measured, and even more so if that "high" sampling rate is in fact low enough to permit the use of the high accuracy analog to digital conversion techniques used in the best laboratory grade voltmeters. In fact, for the measurement of low frequency AC signals (those of say, less than thirty or forty hertz) sampling offers additional advantages pertaining to avoiding the need for large valued coupling capacitances or low drift DC coupled circuitry. In principle, today's high accuracy fast DC voltmeters ought to be usable for making ultra high accuracy (in the vicinity of ten parts per million) measurements (e.g., RMS voltage) on low frequency AC signals of about a kilohertz or less in frequency. This degree of potential accuracy is simply beyond all but the most exotic analog techniques.
Digital techniques do, however, introduce their own special difficulties. Among these are issues arising from how well one can control when (i.e., at exactly what times) the samples occur. This is not trivial, since samples are often taken over what is assumed to be exactly one or an integral number of input signal cycles, for which the samples are then processed in an appropriate manner for the type of measurement desired. Since digital systems tend to run with timing controlled by internal clock circuits of fixed frequency (whose period may in fact be the precision quantity upon which the accuracy of the analog to digital conversion process is dependent!) the location of actual samples along a cycle of the input signal may not be convenient for the subsequent processing of the samples. What is more, it may not be possible to shift those locations to be convenient.
For example, the method of measurement may require that the samples (1) be equally spaced; and (2) that the number of samples taken match exactly one cycle of the signal to be measured. (That is, the sample-to-sample interval exactly divides the signal period; such sampling may be termed aliquot sampling.) The first requirement of equal spacing of the samples is not generally a problem, but the second requirement can cause considerable trouble. This trouble arises because of the fixed frequency clocked operation and internal overhead for control of the analog to digital conversion process on the one hand, and on the other hand because of the ability of the signal being measured to have a totally arbitrary period. As a specific example, it may be possible to cause the analog to digital converter to space its samples in increments of hundredths or tenths of a second, but this won't meet the second requirement above if the frequency of the signal to be measured is, say, exactly three hertz. The resulting error can be quite significant.
A common cure for the difficulty of the sample interval not exactly dividing the signal period is to make the measurement over a plurality of consecutive signal periods. Either the sample interval will exactly divide (or almost exactly divide) the plurality of periods, in which case the error is never introduced and the answer is the average of the plurality, or the inexactitude remains as before but is now distributed across the contributions of each of the cycles in the average, and is thus reduced according to the number of periods in the average.
There are some disadvantages with this approach, however. Suppose that the signal period is long, say several seconds or several tens of seconds. Further, it may be that the sample interval and the signal period are such that several hundred, or even a thousand or so, signal periods would be needed to minimize the effects of inexact division by the sample interval. Not only is this inconvenient because of the time required to make the measurement, but it raises some other sticky issues relating to stability: has either the signal or the analog to digital conversion mechanism changed over the course of the measurement?.
In accordance with the invention described herein, it is possible to accurately measure an AC input signal with sampling even though the available sampling intervals do not exactly divide the period of the AC signal to be measured, and to do so without averaging over a plurality of periods which is exactly divisible (or nearly so) by the sampling interval. The invention exploits the observation that regular but inexact sampling for a group of samples over one cycle of the AC input signal produces an answer that can be decomposed into a result+error. The magnitude of the error is a periodic AC function, and its effect will be distributed over successive groups of samples. Thus, if several such answer.sub.i are found such that their corresponding error.sub.i are from locations equally and aliquotly spaced along the period of the error function, the average of the answer.sub.i will be simply the average of the result.sub.i. That is because the error.sub.i will sum to zero (be self-canceling) during the averaging. This aliquot spacing of the error.sub.i can be obtained by aliquot spacing upon the input waveform of the start of the groups of samples. That is, if six groups of samples are to be taken, then each group starts one sixth of an input signal period further along the phase of the input signal than it predecessor.
Deliberate selection of a sampling interval that does not exactly divide the period of the signal to be measured has advantages even when such division would otherwise be possible. Proper selection of an inexact sampling interval can ensure that lowest harmonic component that is aliased by the sampling is ridiculously high in number, thus guaranteeing that all harmonics below a certain number are accounted for by the sampling process, even though the sampling does not strictly meet the Nyquist theorem's requirements for those harmonics. Instead, those harmonics produce errors in the intermediate answers. Those errors can also be made self-canceling by the aliquot spacing of the starting points of the pluralities of the samples upon input waveform.